A smooth edge potential could lead to edge reconstruction of a $\nu =1$ quantum Hall state, resulting in an additional $\nu =1/3$ QH side strip, which, in turn, may yield Majorana/parafermion zero modes at the domain wall of the superconductor and ferromagnet on the edge. We demonstrate that the constraints imposed by the $\nu =1$ bulk permit the existence of multiple types of electron operators, leading to distinct and immutable species of Majorana modes. Different velocities of the reconstructed edge modes provide a clear signature of these species of Majoranas in the $4\pi$ fractional Josephson current.

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• Andreev reflection
• Anyons
• Edge states
• Fractionalization
• Josephson effect
• Topological superconductors
• Two-dimensional electron system
• Bogoliubov-de Gennes equations
• Bosonization
• Luttinger liquid model